Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.

Shape Anisotropy and Resonance Mode Guided Reliable Interconnect Design for In-plane Magnetic Logic

Dipole coupled nanomagnets controlled by the static Zeeman field can form various magnetic logic interconnects.However, the corner wire interconnect is often unreliable and error-prone at room temperature. In this study, we address this problem by making it into a reliable type with trapezoid-shaped nanomagnets, the shape anisotropy of which helps to offer the robustness. The building method of the proposed corner wire interconnect is discussed,and both its static and dynamic magnetization properties are investigated. Static micromagnetic simulation demonstrates that it can work correctly and reliably. Dynamic response results are reached by imposing an ac microwave field on the proposed corner wire. It is found that strong ferromagnetic resonance absorption appears at a low frequency. With the help of a very small ac field with the peak resonance frequency, the required static Zeeman field to switch the corner wire is significantly decreased by ~21 m T. This novel interconnect would pave the way for the realization of reliable and low power nanomagnetic logic circuits.

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

Aircraft designers strive to achieve optimal weight-reliability tradeoffs while designing an aircraft. Since aircraft wing skins account for more than fifty percent of their structural weight, aircraft wings must be designed with utmost care and attention in terms of material types and thickness configurations. In particular, the selection of thickness at each location of the aircraft wing skin is the most consequential task for aircraft designers. To accomplish this, we present discrete mathematical programming models to obtain optimal thicknesses either to minimize weight or to maximize reliability. We present theoretical results for the decomposition of these discrete mathematical programming models to reduce computer memory requirements and facilitate the use of dynamic programming for design purposes. In particular, a decomposed version of the weight minimization problem is solved for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location to yield an optimal minimum weight design.

The Reliability Design of a Kind of Multioption Fuze

On the basis of analysing the reliability problems existing in the general design of a kind of multioption fuze. some problems such as the reliability model. the reliability distribution of the electronic part of the fuze are discussed. For a particular multioption fuze, then.according to three different setting ways. the calculating methods of its operating reliability in six different operating states are given.

Reliability Design for Impact Vibration of Hydraulic Pressure Pipeline Systems

The research of reliability design for impact vibration of hydraulic pressure pipeline systems is still in the primary stage,and the research of quantitative reliability of hydraulic components and system is still incomplete.On the condition of having obtained the numerical characteristics of basic random parameters,several techniques and methods including the probability statistical theory,hydraulic technique and stochastic perturbation method are employed to carry out the reliability design for impact vibration of the hydraulic pressure system.Considering the instantaneous pressure pulse of hydraulic impact in pipeline,the reliability analysis model of hydraulic pipeline system is established,and the reliability-based optimization design method is presented.The proposed method can reflect the inherent reliability of hydraulic pipe system exactly,and the desired result is obtained.The reliability design of hydraulic pipeline system is achieved by computer programs and the reliability design information of hydraulic pipeline system is obtained.This research proposes a reliability design method,which can solve the problem of the reliability-based optimization design for the hydraulic pressure system with impact vibration practically and effectively,and enhance the quantitative research on the reliability design of hydraulic pipeline system.The proposed method has generality for the reliability optimization design of hydraulic pipeline system.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

RESEARCH PROGRESS ON STRUCTURAL FATIGUE RELIABILITY DESIGN AND ANALYSIS METHODS OF CHINESE RAILWAY VEHICLES

A state-of-art review is given to the new advances on fatigue reliability design and analysis methods of Chinese railway vehicle＇s structures. First, the structures are subject to a complicated random fatigue stressing history and this history should be determined by combining dynamic simulation and on-line inspection. Second, the random fatigue constitutions belong to an intrinsic fatigue phenomenon and a probabilistic model is developed to well describe them with two measurements of survival probability and confidence, similar model is also presented for the random stress-life rela- tions and extrapolated appropriately into Song fatigue life regime. Third, concept of the fatigue limit should be understood as the fatigue strength at a given fatigue life and a so-called local Basquin model method is proposed for measuring the random strengths. In addition, drawing and application methods of the Goodman-Smith diagram for integrally characterizing the random fatigue strengths are established in terms of ten kilometers. Fourth, a reliability stress-based method is constructed with a consideration of the random constitutive relations. These new advances form a new frame work for railway fatigue reliability design and analysis.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

Research on Optimal Design for Reliability of Fuze Components

Reliability optimal design is an integrated approach widely adopted in engineering. The fuze components are designed by a BP neural network combined with an optimal design approach based on their multi-failure modes. Their reliability probabilities in multi-failure modes are transformed into deterministic design parameters. The designed results by an example of optimizing the fuze spring under a certain reliability show that the integrated approach is practical and efficient.

Genetic optimization of reliability design of machine element

Canonical genetic algorithms have the defects of prematurity and stagnation when applied in optimization problems. The causes resulting in such phenomena were analyzed and a class of improved genetic algorithm with niche implemented by crossover of similar individuals and ( μ+λ ) selection was proposed. According to the reliability design theory of machine components, the genetic optimization model of jack clutch was obtained. An optimization instance and some results calculated by improved genetic algorithm were presented. The results of emulations and application show that the improved genetic algorithm with the niche technique can achieve the reliable global convergence and stable convergent velocity almost without any additional calculation expense. [

Exponential System Reliability Test Design Based on Information Fusion

By analyzing the shortage of reliability test design and thinking over the producer's risk and consumer's risk, the information fusion technology is used to set up a reliability test design model( RTDM). By analyzing the demands and constraint conditions of the RTDM and with applications of Bayesian approach and Monte Carlo method( MCM),this paper puts forward the exponential distributed subsystems and the information fusion technology among them. According to the posteriori risk criteria,formulas of producer's risk and consumer's risk were also inferred,and with the help of Matlab software,selection of the optimum test plan was solved. Finally,validity of the model had been proved by a test of series parallel system.

A Dynamic Programming Approach to the Design of Composite Aircraft Wings

A light and reliable aircraft has been the major goal of aircraft designers. It is imperative to design the aircraft wing skins as efficiently as possible since the wing skins comprise more than fifty percent of the structural weight of the aircraft wing. The aircraft wing skin consists of many different types of material and thickness configurations at various locations. Selecting a thickness for each location is perhaps the most significant design task. In this paper, we formulate discrete mathematical programming models to determine the optimal thicknesses for three different criteria: maximize reliability, minimize weight, and achieve a trade-off between maximizing reliability and minimizing weight. These three model formulations are generalized discrete resource-allocation problems, which lend themselves well to the dynamic programming approach. Consequently, we use the dynamic programming method to solve these model formulations. To illustrate our approach, an example is solved in which dynamic programming yields a minimum weight design as well as a trade-off curve for weight versus reliability for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location.

Reliability Design of Ice-Maker System Subjected to Repetitive Loading

Parametric Accelerated Life Testing (ALT) was used to improve the reliability of ice-maker system with a fractured helix upper dispenser in field. By using bond graphs and state equations, a variety of mechanical loads in the assembly were analyzed. The acceleration factor was derived from a generalized life-stress failure model with a new load concept. To reproduce the failure modes and mechanisms causing the fracture, new sample size equation was derived. The sample size equation with the acceleration factor also enabled the parametric accelerated life testing to quickly reproduce early failure in field. Consequently, the failure modes and mechanisms found were identical with those of the failed sample. The design of this testing should help an engineer uncover the design parameters affecting the reliability of fractured helix upper dispenser in field. By eliminating the design flaws, gaps and weldline, the B1 life of the redesign of helix upper dispenser is now guaranteed to be over 10 years with a yearly failure rate of 0.1% that is the reliability quantitative test specifications (RQ).

Multi-objective reliability optimization design of high-speed heavy-duty gears based on APCK-SORA model

For high-speed heavy-duty gears in operation is prone to high tooth surface temperature rise and thus produce tooth surface gluing leading to transmission failure and other adverse effects,but in the gear optimization design and little consideration of thermal transmission errors and thermal resonance and other factors,while the conventional multi-objective optimization design methods are difficult to achieve the optimum of each objective.Based on this,the paper proposes a gear multi-objective reliability optimisation design method based on the APCK-SORA model.The PC-Kriging model and the adaptive k-means clustering method are combined to construct an adaptive reliability analysis method(APCK for short),which is then integrated with the SORA optimisation algorithm.The objective function is the lightweight of gear pair,the maximum overlap degree and the maximum anti-glue strength;the basic parameters of the gear and the sensitivity parameters affecting the thermal deformation and thermal resonance of the gear are used as design variables;the amount of thermal deformation and thermal resonance,as well as the contact strength of the tooth face and the bending strength of the tooth root are used as constraints;the optimisation results show that:the mass of the gear is reduced by 0.13kg,the degree of overlap is increased by 0.016 and the coefficient of safety against galling Compared with other methods,the proposed method is more efficient than the other methods in meeting the multi-objective reliability design requirements of lightweighting,ensuring smoothness and anti-galling capability of high-speed heavy-duty gears.

Fuzzy Reliability Design for the Interference Articulation of a Roller Shaft

With regard to function, the strengths for interference articulation of a roller shaft formed a series system. As the three strength reliabilities conditioned each other, there was a problem for the system reliability to apportion rationally. In fact, there was a transition from safety to deactivation. The state of structure was fuzziness which was in both safety and non-safety states. Therefore the reliability was a fuzzy event which considered the randomness for some design parameters and the fuzziness for the thresholds between generalized strength safety and deactivation. The mathematical model of fuzzy reliability design for the interference articulation of the roller shaft was presented. Eight design examples were calculated.

新一代运载火箭分离系统可靠性设计方法研究

The LM-5B carrier rocket is a new-generation large-scale launch vehicle developed for space station launch missions.Its separation system includes fairing separation,space station module-rocket separation,and booster separation.The separation systems play an important role in the design of launch vehicles,and any failure during the separation process would affect the final completion of rocket flight mission.This paper presents the reliability design and analysis for the LM-5B carrier rocket separation system.The LM-5B carrier rocket separation system was developed on the basis of the LM-5 carrier rocket separation system,inheriting its booster separation system and fairing separation system scheme,which maximizes the reliability of the separation system.The reliability of the LM-5B fairing separation system,booster separation system and space station module-rocket separation system can meet the requirements for launch missions.The demonstration results prove that redundant design of the separation systems was the most effective technical means to improve reliability.

Reliability Based Multi-Objective Thermodynamic Cycle Optimisation of Turbofan Engines Using Luus-Jaakola Algorithm

Aircraft engine design is a complicated process,as it involves huge number of components.The design process begins with parametric cycle analysis.It is crucial to determine the optimum values of the cycle parameters that would give a robust design in the early phase of engine development,to shorten the design cycle for cost saving and man-hour reduction.To obtain a robust solution,optimisation program is often being executed more than once,especially in Reliability Based Design Optimisations(RBDO)with Monte-Carlo Simulation(MCS)scheme for complex systems which require thousands to millions of optimisation loops to be executed.This paper presents a fast heuristic technique to optimise the thermodynamic cycle of two-spool separated flow turbofan engines based on energy and probability of failure criteria based on Luus-Jaakola algorithm(LJ).A computer program called Turbo Jet Engine Optimiser v2.0(TJEO-2.0)has been developed to perform the optimisation calculation.The program is made up of inner and outer loops,where LJ is used in the outer loop to determine the design variables while parametric cycle analysis of the engine is done in the inner loop to determine the engine performance.Latin-Hypercube-Sampling(LHS)technique is used to sample the design and model variations for uncertainty analysis.The results show that optimisation without reliability criteria may lead to high probability of failure of more than 11%on average.The thrust obtained with uncertainty quantification was about 25%higher than the one without uncertainty quantification,at the expense of less than 3%of fuel consumption.The proposed algorithm can solve the turbofan RBDO problem within 3 min.

Reliability design optimization of composite structures based on PSO together with FEA

The present work aims to develop a method for reliability-based optimum design of composite structures. A procedure combining particle swarm optimization （PSO） and finite element analysis （FEA） has been proposed. Numerical examples for the reliability design optimization （RDO） of a laminate and a composite cylindrical shell are worked out to demonstrate the effectiveness of the method. Then a design for composite pressure vessels is studied. The advantages and necessity of RDO over the conventional equi-strength design are addressed. Examples show that the proposed method has good stability and is efficient in dealing with the probabilistic optimal design of composite structures. It may serve as an effective tool to optimize other complicated structures with uncertainties.

A method of multi-objective reliability tolerance design for electronic circuits

Tolerance design plays an important role in reliability design for electronic circuits. The traditional method only focuses on the consistency of output response. It is not able to meet the needs of increasing development of electronic products. This paper researches the state of related fields and proposes a method of multi-objective reliability tolerance design. The characteristics of output response and operating stresses on critical components are both defined as design objectives. Critical components and their operating stresses are determined by failure mode and effect analysis （FMEA） and fault tree analysis （FTA）. Sensitivity analysis is carried out to determine sensitive parameters that affect the design objectives significantly. Monte Carlo and worst-case analysis are utilized to explore the tolerance levels of sensitive parameters. Design of experiment and regression analysis are applied in this method. The optimal tolerance levels are selected in accord with a quality-cost model to improve consistency of output response and reduce failure rates of critical components synchronously. The application in light-emitting diode （LED） drivers indicates details and potential. It shows that the proposed method provides a more effective way to improve performance and reliability of electronic circuits.

Application of Conservative Surrogate to Reliability Based Vehicle Design for Crashworthiness

Surrogate models are commonly used for approximation of large computationally expensive vehicle crash simulation to facilitate rapid design space exploration and optimization. Unfortunately, the optimum design based on surrogates may turn out to be infeasible after running finite element crash simulation due to the surrogate errors. To meet this challenge, conservative strategy of surrogate modeling through compensating fitting errors was used for reliability based design optimization of vehicle structures for crashworthiness and weight reduction. The critical crash responses were constructed by unbiased kriging models, and conservative surrogates were obtained via adding safety margin to estimate the crash responses conservatively. The benefits of using conservative surrogates for reliability based design optimization were investigated in the context of constraint feasibility of the optimum designs through a mathematical example and a case study on vehicle crashworthiness design. The results demonstrate that optimization based on conservative surrogate helps to achieve the feasible optimum design, showing more attractive for reliability based design optimization in engineering applications.